Write the multiplicative inverse of :

(i) 9

(ii) -1

(iii) $\dfrac{11}{16}$

(iv) $5\dfrac{1}{4}$

(v) $\dfrac{-2}{3}$

(vi) $17\dfrac{3}{20}$

(vii) $–18\dfrac{1}{2}$

(viii) –5

(ix) $\dfrac{-20}{41}$

The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1.

(i) Let the multiplicative inverse of 9, be x.

⇒ 9 × x = 1

⇒ x = $\dfrac{1}{9}$.

Hence, multiplicative inverse of 9 = $\dfrac{1}{9}$.

(ii) Let the multiplicative inverse of -1, be x.

⇒ -1 × x = 1

⇒ x = $-\dfrac{1}{1}$ = -1.

Hence, multiplicative inverse of -1 = -1.

(iii) Let the multiplicative inverse of $\dfrac{11}{16}$, be x.

⇒ $\dfrac{11}{16}$ × x = 1

⇒ x = $\dfrac{16}{11}$.

Hence, multiplicative inverse of $\dfrac{11}{16} = \dfrac{16}{11}$.

(iv) Let the multiplicative inverse of $5\dfrac{1}{4}$, be x.

⇒ $5\dfrac{1}{4}$ × x = 1

⇒ $\dfrac{21}{4}$ × x = 1

⇒ x = $\dfrac{4}{21}$.

Hence, multiplicative inverse of $5\dfrac{1}{4} = \dfrac{4}{21}$.

(v) Let the multiplicative inverse of $-\dfrac{2}{3}$, be x.

⇒ $-\dfrac{2}{3}$ × x = 1

⇒ x = $-\dfrac{3}{2}$.

Hence, multiplicative inverse of $-\dfrac{2}{3} = -\dfrac{3}{2}$.

(vi) Let the multiplicative inverse of $17\dfrac{3}{20}$, be x.

⇒ $17\dfrac{3}{20}$ × x = 1

⇒ $\dfrac{343}{20}$ × x = 1

⇒ x = $\dfrac{20}{343}$.

Hence, multiplicative inverse of $17\dfrac{3}{20} = \dfrac{20}{343}$.

(vii) Let the multiplicative inverse of $–18\dfrac{1}{2}$, be x.

⇒ $–18\dfrac{1}{2}$ × x = 1

⇒ $-\dfrac{37}{2}$ × x = 1

⇒ x = $–\dfrac{2}{37}$.

Hence, multiplicative inverse of $-18\dfrac{1}{2} = -\dfrac{2}{37}$.

(viii) Let the multiplicative inverse of –5, be x.

⇒ –5 × x = 1

⇒ x = $-\dfrac{1}{5}$.

Hence, multiplicative inverse of $-5 = -\dfrac{1}{5}$.

(ix) Let the multiplicative inverse of $\dfrac{-20}{41}$, be x.

⇒ $\dfrac{-20}{41}$ × x = 1

⇒ x = $-\dfrac{41}{20}$.

Hence, multiplicative inverse of $-\dfrac{20}{41} = -\dfrac{41}{20}$.